我正在测试一个根据 Simon Funk 算法构建的推荐系统。 （作者及时开发。http://www.timelydevelopment.com/demos/NetflixPrize.aspx）
问题是，所有增量 SVD 算法都试图预测 user_id 和 movie_id 的评分。但在实际系统中，这应该为活动用户生成一个新项目列表。 我看到有些人在 Incremental SVD 之后使用了 kNN，但是如果我没有遗漏一些东西，如果我在通过 Incremental SVD 创建模型之后使用 kNN，我会失去所有的性能提升。
有人对增量 SVD/Simon Funk 方法有任何经验，请告诉我如何生成新推荐项目列表？
【问题讨论】：
标签： recommendation-engine collaborative-filtering svd knn
推荐电影的制作方式：
对于理论：假设只有两个维度（喜剧和戏剧）。如果我喜欢喜剧，但讨厌戏剧，我的特征向量是[1.0, 0.0]。如果您将我与以下电影进行比较：
Comedy: [1.0, 0.0] x [1.0, 0.0] = 1
Dramedy: [0.5, 0.5] x [1.0, 0.0] = 0.5
Drama: [0.0, 1.0] x [1.0, 0,0] = 0
【讨论】：
这是一个基于 Yelp Netflix 代码的简单 Python 代码。如果您安装 Numba，它将以 C 速度运行。
data_loader.py
import os
import numpy as np
from scipy import sparse
class DataLoader:
def __init__(self):
pass
@staticmethod
def create_review_matrix(file_path):
data = np.array([[int(tok) for tok in line.split('\t')[:3]]
for line in open(file_path)])
ij = data[:, :2]
ij -= 1
values = data[:, 2]
review_matrix = sparse.csc_matrix((values, ij.T)).astype(float)
return review_matrix
movielens_file_path = '%s/Downloads/ml-100k/u1.base' % os.environ['HOME']
my_reviews = DataLoader.create_review_matrix(movielens_file_path)
user_reviews = my_reviews[8]
user_reviews = user_reviews.toarray().ravel()
user_rated_movies, = np.where(user_reviews > 0)
user_ratings = user_reviews[user_rated_movies]
movie_reviews = my_reviews[:, 201]
movie_reviews = movie_reviews.toarray().ravel()
movie_rated_users, = np.where(movie_reviews > 0)
movie_ratings = movie_reviews[movie_rated_users]
user_pseudo_average_ratings = {}
user_pseudo_average_ratings[8] = np.mean(user_ratings)
user_pseudo_average_ratings[9] = np.mean(user_ratings)
user_pseudo_average_ratings[10] = np.mean(user_ratings)
users, movies = my_reviews.nonzero()
users_matrix = np.empty((3, 3))
users_matrix[:] = 0.1
movies_matrix = np.empty((3, 3))
movies_matrix[:] = 0.1
result = users_matrix[0] * movies_matrix[0]
otro = movies_matrix[:, 2]
otro[2] = 8
funk.py
# Requires Movielens 100k data
import numpy as np, time, sys
from data_loader import DataLoader
from numba import jit
import os
def get_user_ratings(user_id, review_matrix):
"""
Returns a numpy array with the ratings that user_id has made
:rtype : numpy array
:param user_id: the id of the user
:return: a numpy array with the ratings that user_id has made
"""
user_reviews = review_matrix[user_id]
user_reviews = user_reviews.toarray().ravel()
user_rated_movies, = np.where(user_reviews > 0)
user_ratings = user_reviews[user_rated_movies]
return user_ratings
def get_movie_ratings(movie_id, review_matrix):
"""
Returns a numpy array with the ratings that movie_id has received
:rtype : numpy array
:param movie_id: the id of the movie
:return: a numpy array with the ratings that movie_id has received
"""
movie_reviews = review_matrix[:, movie_id]
movie_reviews = movie_reviews.toarray().ravel()
movie_rated_users, = np.where(movie_reviews > 0)
movie_ratings = movie_reviews[movie_rated_users]
return movie_ratings
def create_user_feature_matrix(review_matrix, NUM_FEATURES, FEATURE_INIT_VALUE):
"""
Creates a user feature matrix of size NUM_FEATURES X NUM_USERS
with all cells initialized to FEATURE_INIT_VALUE
:rtype : numpy matrix
:return: a matrix of size NUM_FEATURES X NUM_USERS
with all cells initialized to FEATURE_INIT_VALUE
"""
num_users = review_matrix.shape[0]
user_feature_matrix = np.empty((NUM_FEATURES, num_users))
user_feature_matrix[:] = FEATURE_INIT_VALUE
return user_feature_matrix
def create_movie_feature_matrix(review_matrix, NUM_FEATURES, FEATURE_INIT_VALUE):
"""
Creates a user feature matrix of size NUM_FEATURES X NUM_MOVIES
with all cells initialized to FEATURE_INIT_VALUE
:rtype : numpy matrix
:return: a matrix of size NUM_FEATURES X NUM_MOVIES
with all cells initialized to FEATURE_INIT_VALUE
"""
num_movies = review_matrix.shape[1]
movie_feature_matrix = np.empty((NUM_FEATURES, num_movies))
movie_feature_matrix[:] = FEATURE_INIT_VALUE
return movie_feature_matrix
@jit(nopython=True)
def predict_rating(user_id, movie_id, user_feature_matrix, movie_feature_matrix):
"""
Makes a prediction of the rating that user_id will give to movie_id if
he/she sees it
:rtype : float
:param user_id: the id of the user
:param movie_id: the id of the movie
:return: a float in the range [1, 5] with the predicted rating for
movie_id by user_id
"""
rating = 1.
for f in range(user_feature_matrix.shape[0]):
rating += user_feature_matrix[f, user_id] * movie_feature_matrix[f, movie_id]
# We trim the ratings in case they go above or below the stars range
if rating > 5: rating = 5
elif rating < 1: rating = 1
return rating
@jit(nopython=True)
def sgd_inner(feature, A_row, A_col, A_data, user_feature_matrix, movie_feature_matrix, NUM_FEATURES):
K = 0.015
LEARNING_RATE = 0.001
squared_error = 0
for k in range(len(A_data)):
user_id = A_row[k]
movie_id = A_col[k]
rating = A_data[k]
p = predict_rating(user_id, movie_id, user_feature_matrix, movie_feature_matrix)
err = rating - p
squared_error += err ** 2
user_feature_value = user_feature_matrix[feature, user_id]
movie_feature_value = movie_feature_matrix[feature, movie_id]
#for j in range(NUM_FEATURES):
user_feature_matrix[feature, user_id] += \
LEARNING_RATE * (err * movie_feature_value - K * user_feature_value)
movie_feature_matrix[feature, movie_id] += \
LEARNING_RATE * (err * user_feature_value - K * movie_feature_value)
return squared_error
def calculate_features(A_row, A_col, A_data, user_feature_matrix, movie_feature_matrix, NUM_FEATURES):
"""
Iterates through all the ratings in search for the best features that
minimize the error between the predictions and the real ratings.
This is the main function in Simon Funk SVD algorithm
:rtype : void
"""
MIN_IMPROVEMENT = 0.0001
MIN_ITERATIONS = 100
rmse = 0
last_rmse = 0
print len(A_data)
num_ratings = len(A_data)
for feature in xrange(NUM_FEATURES):
iter = 0
while (iter < MIN_ITERATIONS) or (rmse < last_rmse - MIN_IMPROVEMENT):
last_rmse = rmse
squared_error = sgd_inner(feature, A_row, A_col, A_data, user_feature_matrix, movie_feature_matrix, NUM_FEATURES)
rmse = (squared_error / num_ratings) ** 0.5
iter += 1
print ('Squared error = %f' % squared_error)
print ('RMSE = %f' % rmse)
print ('Feature = %d' % feature)
return last_rmse
LAMBDA = 0.02
FEATURE_INIT_VALUE = 0.1
NUM_FEATURES = 20
movielens_file_path = '%s/Downloads/ml-100k/u1.base' % os.environ['HOME']
A = DataLoader.create_review_matrix(movielens_file_path)
from scipy.io import mmread, mmwrite
mmwrite('./data/A', A)
user_feature_matrix = create_user_feature_matrix(A, NUM_FEATURES, FEATURE_INIT_VALUE)
movie_feature_matrix = create_movie_feature_matrix(A, NUM_FEATURES, FEATURE_INIT_VALUE)
users, movies = A.nonzero()
A = A.tocoo()
rmse = calculate_features(A.row, A.col, A.data, user_feature_matrix, movie_feature_matrix, NUM_FEATURES )
print 'rmse', rmse
【讨论】：
我认为这是一个大问题，因为有很多推荐方法我认为可以称为“增量 SVD”。回答您的具体问题：kNN 在投影项目空间上运行，而不是在原始空间上运行，所以应该很快。
【讨论】：
假设您有 n 个用户和 m 个项目。在增量 SVD 之后，你有 k 个训练好的特征。要获得给定用户的新商品，请将 1xk 用户特征向量和 kxm 商品特征矩阵相乘。您最终得到该用户的每个项目的 m 个评分。然后对它们进行排序，删除他们已经看过的，并显示一些新的。
【讨论】：